Rick, thank you for your reply. Tom Gibson on the FlightSim forum has given me the answer. In the first model that I made, the Import process "automatically" filled in the Night Texture section of the Material Editor. So, when the other imports did not do this, I of course did not realized that, so I had no idea what was "wrong".
To answer your question, this is what I did. Import the flyable.mdl file. Fix all the animations into the positions I wanted them. Export the result into a static.bgl as a Scenery Object. That is *all* that I did. And it worked fine, as it always has. The only thing that was "wrong" was that it did not use the night textures. I did absolutely nothing with textures. In fact the whole point of this was to end up with a static model that looks exactly like the flyable one!
You might have misunderstood one thing I said; mea culpa, my bad phrasing. When I said that the default 737-400 "did not work", I only meant in the sense that it did not load the night lighting. Other than that, it converted completely and correctly.
You ask about the Mike Stone models. I have his fabulous and quite hilarious B52M, so I tried it with that. Both MCX versions did not load the _L.bmp files, which are supplied with that model.
I see this as an error in MCX. The error is in the inconsistency. That for some models it automatically assigns night textures, for others, it does not. This is quite clear from the event log. In some cases it "preemptively" opens the _L files on import; in most cases, it does not. I have both Stable Release 1.3.0.0, and 1.4.0.0 DEV 4/01/2015; they both behave the same way in this regard.
Having said all that, once you know the solution, it is a minor error. You're not going to make hundreds of different static models every day! And even the most complex models have only a handful of files. Having to fill in one data field per texture file via a Select_File is not that onerous a task.